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JERUSALEM — The street revolt in Egypt has thrown the Israeli government and military into turmoil, with top officials closeted in round-the-clock strategy sessions aimed at rethinking their most significant regional relationship.

Israel’s military planning relies on peace with Egypt. Nearly half the natural gas it uses is imported from Egypt, and the principle of trading conquered land for diplomatic ties began with its 1979 peace treaty with Egypt.

Prime Minister Benjamin Netanyahu has met with President Hosni Mubarak of Egypt more than with any other foreign leader, except President Obama. If Mubarak were driven from power, the effect on Israel could be profound.

“For the United States, Egypt is the keystone of its Middle East policy,’’ a senior official said. “For Israel, it’s the whole arch.’’

The official spoke on condition of anonymity because Netanyahu has ordered his ministers and their officials to stay publicly silent on Egypt while events there play out.

Many analysts in Israel said that even if Mubarak were forced to leave office, those who replace him could maintain Egypt’s peace treaty with Israel, since it is the basis for more than $1 billion in annual aid to Cairo from Washington and much foreign investment.

But others noted that the best organized political force in Egypt is the Muslim Brotherhood, which is hostile to Israel and close to Hamas, the Palestinian rulers in Gaza whose weapons smuggling the Egyptian government works to block.

As the government evacuated from Egypt the families of envoys over the weekend, public affairs broadcasts and newspapers in Israel focused heavily on the unfolding events there. Most of the predictions were dire.

Events of the past five years — the takeover of Gaza by Hamas, the rise of Hezbollah in Lebanon, Iran’s influence in Iraq, and Turkey’s shift toward Iran and Syria — have turned many Israelis rightward, fearing that the more time passes, the more the region is against them.

Israelis worry that Jordan is in a precarious state and that a successful overthrow in Egypt could spread there. And if the Muslim Brotherhood were to gain power in Egypt, it would probably mean not only a stronger Islamist force in Gaza but also in the West Bank, currently run by the Fatah-dominated Palestinian Authority, as well as in Jordan, meaning Israel would feel surrounded in a way it has not in decades.

Also, if Egypt turned unfriendly, it would likely stop any further Israeli talk of peace negotiations with the Palestinians, officials and analysts said.

There has long been concern that popular sentiment in Egypt is anti-Israel. Eli Shaked, a former Israeli ambassador to Cairo, wrote in Yediot Aharonot newspaper: “The only people in Egypt who are committed to peace are the people in Mubarak’s inner circle, and if the next president is not one of them, we are going to be in trouble.’’

Netanyahu could be left without an ally in the region. Prime Minister Recep Tayyip Erdogan of Turkey is angry with Israel because of the Gaza war two years ago and in particular after Israeli commandos killed nine Turks aboard a flotilla trying to break Israel’s blockade of Gaza last May.

King Abdullah II of Jordan, while maintaining peaceful relations with Israel, has also been critical of Netanyahu.

For the military here, a serious change in Egypt means a strategic shift in planning.

Giora Eiland, a former national security adviser and senior fellow at Tel Aviv University, said even if Egypt did not cancel its peace treaty with Israel, a government dominated by the Muslim Brotherhood would mean “you can’t exclude the possibility of a war with Egypt.